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Place an X into seven of the squares so that no square marked with an X is halfway between two other squares that are also marked with an X.
In the diagram below, the number five is made up of 5 identical line segments. Reposition the line segments so the number five appears 5 times. You are not allowed to do anything except moving th...
In the 4x4 grid below, fill each empty square with a number such that the numbers in each row form an arithmetic progression when read from left to right. Similarly, the numbers in each column shou...
Eight different dominoes lie on a plane. No boundaries between the dominoes are shown in the figure. Draw these boundaries. Clarifications: A domino is made up two square halves joined at a com...
In a bag are 26 bills. If you take out 20 bills from the bag at random, you are guaranteed to have at least one 1-dollar bill, two 2-dollar bills, and five 5-dollar bills. How much money was in t...
Using the numbers $3, \ 7, \ 25, \ 50, \ 75, \ 100$ (each used at most once), along with any number of the four basic arithmetic operations (addition, subtraction, multiplication and division) and ...
There are 6 permutations of the numbers 1, 2, 3. They are: 123 132 213 231 312 321 The goal is to make a string (as short as possible) using the digits 1, 2 and 3 so that each of the abov...
In the diagram below we have pentagon ABCDE with 5 edges and 5 diagonals. These 10 line segments are currently all colored black. The diagram contains several triangles but for this puzzle we are...
A large whiteboard has 2014 "+" signs and 2015 "−" signs written on it. You are allowed to delete two of the symbols and replace them according to the following two rules. If the two deleted symbo...
An Amazon is a fairy chess piece that can move like a queen or a knight. What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another? Attribu...
We had a sidewalk and driveway replaced this summer (standard concrete sidewalk, nothing fancy). We've been told not to use salt for at least the first winter because it will damage the young conc...
A 3 by 3 grid contains each digit exactly once, except one missing digit. A 3 by 3 arrangement of 9 such grids has one missing digit per grid. Each digit is missing from exactly one grid, except o...
I disguised some words by shifting each of the letters the same number of steps through the alphabet, but then I forgot the number. Can you find it and restore the original words? vjsygfkusdwksjwi...
Each instance of the word "banana" is in a straight line in one of the 8 directions displayed below: a . . . . . . . a . . . . . . . . a . n . . . . . . n . . . . . . . n . . . a . . . ...
Sometimes after I solve a Wordle puzzle I'll see what their bot had to say about my solution. Occasionally one of my words is a legitimate five-letter word (accepted by Wordle) but the bot says so...
Grid This puzzle is played on a 5 by 5 grid of squares: Tiles There are 25 tiles to be placed on the grid, one on each square. They can each be rotated by any multiple of 90 degrees. Note ...
In the diagram below, there are two types of L-shaped pieces (one made of 5 unit squares and the other made of 7 unit squares). The goal is to tile a 6x9 rectangle with one or more of the smaller ...
Find three different integers A, B and C such that A+B, A+C and B+C are all powers of 2. Clarifications: A, B and C can be negative, zero or positive. Powers of 2 are: 1, 2, 4, 8, 16, ...
Do they have an alert system or the site owner are likely have to detect themselves and report to the vendor? How do they fix the problem? And do they do that for free? As the site owners are their...
Draw 8 straight line segments so that each line segment intersects with exactly 3 other line segments.
Consider the following L-shaped 3-dimensional object consisting of 3 unit cubes joined at their faces: Is it possible to use six of the above L-shaped pieces to form the following 3-dimensiona...
There are $146$ marbles in a bucket. Delta and Epsilon play a game in which they take turns removing marbles from the bucket with Delta going first. At each turn the player can choose to remove e...
There are $100$ marbles in a bucket. Alpha and Beta play a game in which they take turns removing marbles from the bucket with Alpha going first. At each turn the player can choose to remove eith...
Consider the following L-shaped 3-dimensional object made up of three unit cubes joined at their faces: Puzzle 1. Use 9 of the above L-shaped pieces to make a cube. Puzzle 2. Use 10 of the ...
This post describes a classic puzzle. If you have previously seen this puzzle I request that you allow someone else to solve it and post their answer. Thank you! Mutilated chessboard problem: ...
So I was designing this superhuman criminal whose largely just a common burgler. As I was designing her and her powers, eventually I thought of the idea of batwings on the back largely because I th...
A number $\large X$ is defined to be a Droppable Square number if the ordinary base-10 representation of $\large X^2$ can be formed by inserting the digit $\large 2$ anywhere in the base-10 represe...
Consider the following L-shaped piece made of three unit squares joined at their edges: Allowing rotations of the L-shaped pieces, you can easily tile a 2x3 rectangle with two of the above L-sha...
What does the following image represent? Description of above image for those who can’t view it: On the left: Horizontal line with a green happy face above it and a green letter K below it. ...
Join the pairs of dots marked similarly (i.e. A to A, B to B, etc.) using four lines which do not cross or touch at any point. The routes must follow the lines of the grid, and may not pass through...
My fifth is an organ, it's revelatory, My sixth from a slitherer telling its story. My first lacks aspiration but's bringing it still, You’re half way to working this out if you will. My third ...
Puzzle How short can you make a closed knight’s sightseeing tour? Terminology Standard terminology A chess board is an 8 by 8 chequerboard. A knight is a chess piece that moves 2 squares hor...
Draw 3 lines, not necessarily straight, connecting the dots and satisfying all the following conditions: No line may touch or intersect another line. Every line must be completely inside the ci...
In each puzzle, fill the circles using all the positive integers 1, 2, 3, ... n, where n is the number of circles in such a way that consecutive numbers are NOT in circles that are joined with a li...
Here’s a cute puzzle you can share with children. Can you find the intruder?
Fill all 16 squares with a number so that every row, every column and every 2x2 box contains all the numbers 1, 2, 3 and 4 each exactly once. Also the sum of the numbers in the six squares marked ...
Fill each empty square with a number so that every row, every column and every irregularly shaped region contains all the numbers 1, 2, 3, 4 and 5 each exactly once. If you enjoyed this puzzle...
Draw a straight line through the center of the circle below to subdivide it into two halves so that each half will have the same number of occurrences of the letter A. Also each half will have the...
Three perfectly logical women, one of them blind, walk into a completely dark room full of hats. They all know that two of the hats are red and the rest are black. Each woman randomly selects...
A blind person is handed a deck of 52 playing cards and told that exactly 10 of these cards are facing up. How can they divide the cards into two piles, not necessarily of equal size, with each...
Find the pattern in the fingers:
Place the 9 tiles in the 3 by 3 grid. The curved lines on the tiles must divide the grid. The regions the grid is split into must contain equal numbers of dots. The curved lines may stop at th...
Place each of the 9 tiles into the 3 by 3 grid of squares. Each tile may be rotated by any multiple of 90 degrees. Each line on each tile must either meet the edge of the grid or be matched aga...
Arrange the 9 tiles in a 3 by 3 grid so that the lines on them have no loose ends. A line may leave the edge of the grid provided it rejoins on the opposite edge at the same position (the same h...
Arrange the provided polyominoes on a 5 by 5 grid of squares so that there are zero empty squares. The grid The grid is composed of 25 empty squares, arranged in 5 rows and 5 columns. The poly...
The area of a triangle can be calculated as half of the length of its base multiplied by its perpendicular height. This means that two triangles with the same length base and the same perpendicular...
For each of these Make 24 puzzles, use each of the four given numbers exactly once, combined only with addition, subtraction, multiplication, or division to make an expression whose value equals 24...
What number belongs at ? in this sequence? 24 28 33 34 32 36 35 46 52 53 13 11 17 16 18 14 22 ? 33 19 24 Attribution: Nob Yoshigahara in The Mathemagician and Pied Puzzler A Colle...
What part of Toronto is in Peru?
If from six you take nine, and from nine you take ten, (You youths, now the mystery explain;) And if fifty from forty be taken, there then Shall just half a dozen remain. The above puz...
